{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean-Variance Optimization\n",
    "\n",
    "In this notebook I implement the classical **mean-variance optimization** (MVO) algorithm that finds the optimal weights of a portfolio.     \n",
    "For a theoretical background see [modern portfolio theory](https://en.wikipedia.org/wiki/Modern_portfolio_theory).\n",
    "\n",
    "\n",
    "## Contents\n",
    "   - [Loading data and parameter definition](#sec1) \n",
    "   - [Some mathematics](#sec2)\n",
    "   - [Optimization with scipy.optimize](#sec3)\n",
    "     - [Optimize the Sharpe ratio](#sec3.1)\n",
    "     - [Optimal weights between stocks and bond](#sec3.2)\n",
    "   - [Optimization with cvxpy](#sec4) \n",
    "   - [Probability density of the tangency portfolio](#sec5) \n",
    "   - [Short positions - closed formula](#sec6) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import cvxpy as cp\n",
    "import scipy.stats as ss\n",
    "import seaborn as sns\n",
    "import warnings\n",
    "from scipy.optimize import Bounds, LinearConstraint, minimize\n",
    "from IPython.display import display\n",
    "from functions.portfolio_optimization import optimal_weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "## Loading data and parameter definition\n",
    "\n",
    "In the following I define the investment horizon of **1 month** and the risk free monthly return **Rf**.    \n",
    "I also load the time series of daily prices from *filename*, and print the names of the stocks considered in the analysis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = \"data/stocks_data.csv\"\n",
    "investment_horizon = 252/12           # 252 days / 12 months = 1 month\n",
    "Rf = 0.01 / 12                        # annual rate / 12 months"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are NO NaNs\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>JPM</th>\n",
       "      <th>GLD</th>\n",
       "      <th>DIS</th>\n",
       "      <th>VNO</th>\n",
       "      <th>FB</th>\n",
       "      <th>UBS</th>\n",
       "      <th>KO</th>\n",
       "      <th>MCD</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>GM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [AAPL, AMZN, GOOGL, JPM, GLD, DIS, VNO, FB, UBS, KO, MCD, ^GSPC, GM]\n",
       "Index: []"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(filename, index_col=\"Date\", parse_dates=True)\n",
    "stocks = data.columns\n",
    "N = len(stocks)\n",
    "print(\"There are NaNs\") if data.isna().any(axis=1).any(axis=0) else print(\"There are NO NaNs\")\n",
    "pd.DataFrame(columns=stocks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the number of stocks is small, it could be useful to plot the normalized time series and the correlation matrix of the log-returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_ret = np.log( data/data.shift() )[1:]       # compute log-returns "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,6))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "for stk in stocks:\n",
    "    ax1.plot( data[stk]/data[stk][0], label=stk )\n",
    "ax1.legend(); ax1.xaxis.set_tick_params(rotation=45)\n",
    "sns.heatmap(log_ret.corr(), annot=True, cmap=\"YlGnBu\", ax=ax2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "## Some mathematics\n",
    "\n",
    "Let us indicate the stock price at time $t$ with $S_t$.     \n",
    "We can now recall some important definitions:\n",
    "\n",
    "#### Log returns\n",
    "\n",
    "$$ L_t := \\log \\frac{S_t}{S_{t-1}} $$\n",
    "\n",
    "#### Linear returns\n",
    "\n",
    "$$ R_t := \\frac{S_t - S_{t-1}}{S_{t-1}} = \\frac{S_t}{S_{t-1}} -1  $$\n",
    "\n",
    "There are two important properties to remember:\n",
    "\n",
    "1) Thanks to the properties of logarithms, for $t_0 = 0 < t_1 < ... < t_n = T$ we can write:\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "L_T &= \\log \\frac{S_T}{S_{0}} \\\\\n",
    "&= \\log \\bigg( \\frac{S_{t_1}}{S_{t_0}} \\cdot \\frac{S_{t_2}}{S_{t_1}} \\cdot \\frac{S_{t_3}}{S_{t_2}} ....\\frac{S_{t_n}}{S_{t_{n-1}}} \\bigg) \\\\\n",
    "&= \\log \\frac{S_{t_1}}{S_{0}} + \\log \\frac{S_{t_2}}{S_{t_1}} + ... + \\log \\frac{S_{T}}{S_{t_{n-1}}} \\\\\n",
    "&= \\sum_{i=1}^n \\log \\frac{S_{t_{i}}}{S_{t_{i-1}}} = \\sum_{i=1}^n L_{t_i}. \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "2) If we have a **portfolio** $P_t$ with $N$ stocks, we can prove that the linear return of the portfolio at time $t$ before rebalancing (with weights selected at time $t-1$) is:\n",
    "\n",
    "$$ R_t^P = \\sum_{i=1}^N w_{t-1}^i R_t^i $$\n",
    "\n",
    "Let us consider an investor with a total capital $C$ in cash at time $t=0$.     \n",
    "At time $t \\geq 0$ he decides to buy $\\alpha_t^i$ shares of the stock $S_t^i$. Of course the conditions \n",
    "\n",
    "$$ P_t = \\sum_{i=1}^N \\alpha_t^i \\, S_t^i \\quad \\text{and} \\quad P_0 = C $$\n",
    "\n",
    "must hold. It convenient to define the **relative weights** of the portfolio:\n",
    "\n",
    "$$ w_t^i := \\frac{\\alpha_t^i \\, S_t^i}{P_t} $$\n",
    "\n",
    "such that for each $t\\geq0$ \n",
    "\n",
    "$$ \\sum_{i=1}^N w_t^i = 1.$$     \n",
    "\n",
    "At this point it is easy to prove the initial expression:\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sum_{i=1}^N w^i_{t-1} R_t^i  &= \\sum_{i=1}^N  w_{t-1}^i \\biggl( \\frac{S^i_t}{S^i_{t-1}} -1 \\biggr)  \n",
    "= \\sum_{i=1}^N \\frac{\\alpha_{t-1}^i \\, S_{t-1}^i}{P_{t-1}} \\frac{S^i_t}{S^i_{t-1}} - 1 \\\\ \n",
    "&= \\frac{ \\sum_{i=1}^N \\alpha_{t-1}^i \\, S_{t}^i}{P_{t-1}} - 1 \\\\\n",
    "&= \\frac{P_t}{P_{t-1}} - 1 = R^P_t\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where in $\\sum_{i=1}^N \\alpha_{t-1}^i \\, S_{t}^i = P_t$ the values $\\alpha_{t-1}^i$ are the number of shares selected at time $t-1$ i.e. before the rebalancing. \n",
    "\n",
    "### Why did I recall these formulas?\n",
    "\n",
    "Simply because\n",
    "\n",
    "$$ L_t^P \\neq \\sum_{i=1}^N w_{t-1}^i L_t^i \\quad \\text{and} \\quad R_T \\neq \\sum_{i=1}^n R_{t_i} $$\n",
    "\n",
    "therefore **DO NOT USE THEM** with the equal sign!! \n",
    "\n",
    "Ok... if the time interval is short...we can use the first order Taylor approximation of the logarithmic function\n",
    "$\\log(1+x) \\approx x$ such that:\n",
    "\n",
    "$$ L_t = \\log(1 + R_t )   = \\log(1+ \\frac{S_t-S_{0}}{S_{0}}) \\underset{t\\to 0}{\\approx} R_t  $$\n",
    "\n",
    "and linear returns are not so different from the log-returns.     \n",
    "But if we consider monthly or annual returns, the difference becomes significant!\n",
    "\n",
    "\n",
    "#### 1) We use log-returns to estimate the monthly mean and covariance matrix.\n",
    "\n",
    "We can assume that the daily log-returns of $S^i$ are i.i.d. with mean $\\mu^i$ and standard deviation $\\sigma^i$.      \n",
    "Later, we will also assume that the log-returns are normally distributed, but the reality is that this assumption is wrong! \n",
    "If we try to test for normality using Shapiro-Wilk (here below), we can see that for each time series this assumption is rejacted.     \n",
    "Well, this is a well known fact. I didn't waste time writing my Lévy processes notebooks :) \n",
    "\n",
    "We can calculate the monthly mean and covariance matrix from the daily mean and covariance matrix:\n",
    "\n",
    "$$ \\mathbb{E}[L^j_T] = \\mathbb{E}\\biggl[\\sum_{i=1}^n L^j_{t_i}\\biggr] = \\sum_{i=1}^n \\mathbb{E}[L^j_{t_i}] = n \\mu^j $$\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\text{COV}\\biggl[ L^j_T, L^k_T\\biggr] &= \\text{COV} \\biggl[ \\sum_{i=1}^n L^j_{t_i}, \\sum_{i=1}^n L^k_{t_i} \\biggr]  \\\\\n",
    "&= \\sum_{i=1}^n \\text{COV} \\biggl[ L^j_{t_i}, L^k_{t_i} \\biggr] = n\\, \\rho^{j,k} \\sigma^j \\sigma^k = n \\, \\Sigma^{j,k}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where I used the i.i.d. property of log-returns such that $\\text{COV} \\biggl[ L^j_{t_i}, L^k_{t_h} \\biggr] = 0 $ for $i\\neq h$.     \n",
    "The term $\\rho^{j,k}$ is the correlation coefficient between the daily log-returns $L^j$ and $L^k$, and $\\Sigma^{j,k}$ the daily covariance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normality test fails with log-returns. Pvalues:\n",
      " [4.249098360491199e-13, 1.0232545832877804e-07, 1.1264252741281441e-13, 4.622947536831953e-16, 2.722110210851003e-11, 1.9630867349301187e-16, 4.91316272978055e-16, 4.408891220858413e-12, 7.546176293023567e-16, 8.741717134777387e-15, 8.642789107682717e-23, 5.612358417626351e-20, 3.866204977150643e-14]\n"
     ]
    }
   ],
   "source": [
    "pvalues = []\n",
    "for stk in stocks:\n",
    "    pvalues.append( ss.shapiro(log_ret[stk]).pvalue )\n",
    "print(\"Normality test fails with log-returns. Pvalues:\\n\", pvalues)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2) We use monthly linear returns to compute the monthly portfolio linear return.\n",
    "\n",
    "Once we obtained the monthly log-returns, we need to convert them into linear returns.\n",
    "For this purpose, we can assume that log-returns are normally distributed. It follows that the prices are log-normally distributed and linear returns as well: \n",
    "\n",
    "$$ R_t = e^{L_t} - 1 \\sim \\text{lognormal} $$\n",
    "\n",
    "The formulas for the mean and covariance of the multivariate distribution can be found on [wiki](https://en.wikipedia.org/wiki/Log-normal_distribution#Multivariate_log-normal).     \n",
    "Let us call $\\mu_T$ and $\\Sigma_T$ the mean and covariance of the monthly log-returns. The monthly linear returns have: \n",
    "\n",
    "$$ \\mathbb{E}[L^j_T] =   e^{\\mu_T + \\frac{1}{2} \\Sigma_T^{j,j} } - 1 $$\n",
    "\n",
    "$$ \n",
    "\\text{COV} \\biggl[ L^j_T, L^k_T\\biggr] = e^{\\mu_T^j + \\mu_T^k + \\frac{1}{2}(\\Sigma_T^{j,j} + \\Sigma_T^{k,k}) }\n",
    "\\biggl( e^{\\Sigma_T^{j,k}} - 1 \\biggr)\n",
    "$$\n",
    "\n",
    "This topic is also discussed in detail in [1] (see equation 6.162). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# log-return monthly mean and covariance\n",
    "mu_log = investment_horizon * log_ret.mean().values\n",
    "cov_log = investment_horizon * log_ret.cov().values \n",
    "\n",
    "# linear return monthly mean and covariance\n",
    "MU = np.exp(  (mu_log + 0.5 * np.diag(cov_log) ) ) - 1             \n",
    "COV = np.diag(MU+1) @ (np.exp(cov_log) - 1) @ np.diag(MU+1)        # COV written in matrix form"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance of the portfolio\n",
    "\n",
    "The expected return of the portfolio is simply the weighted sum of the expected returns of each stock (here I use the subscript $i$ to simplify the notation)\n",
    "\n",
    "$$ \\mathbb{E}[ R^P ] = \\sum_{i=1}^N w_i \\, \\mathbb{E}[R_i]. $$\n",
    "\n",
    "But the variance involves all the covariance terms:\n",
    "\n",
    "$$ \\text{VAR}[ R^P ] = \\text{VAR}\\biggl[ \\sum_{i=1}^N w_i \\,R_i \\biggr] = \\sum_{i=1}^N w_i^2 \\, \\text{VAR}[R_i] + \\sum_{i,j=1\\\\ \\, i\\not=j}^N w_i w_j \\, \\text{COV}[R_i, R_j] . $$\n",
    "\n",
    "There are $N$ variance terms and $\\frac{N(N-1)}{2}$ covariance terms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3'></a>\n",
    "# Optimization with scipy.optimize\n",
    "\n",
    "Let us write the optimization problem in matrix form.      \n",
    "Let $\\boldsymbol{\\mu}$ and $\\mathbf \\Sigma$ be the expected returns vector and the covariance matrix. Let $\\mathbf w$ be the vector of weights. With $\\mu^P$ I indicate the target portfolio return.      \n",
    "Then the optimization problem can be written as:\n",
    "\n",
    "$$  \\min_{\\mathbf w} \\; \\mathbf w^T \\mathbf \\Sigma \\, \\mathbf w \\quad \\text{subject to } \\quad \\boldsymbol \\mu^T \\mathbf w = \\mu^P, \\quad \\mathbf w^T \\mathbf 1 = 1 \\quad \\text{and} \\quad \\boldsymbol w \\geq 0. $$\n",
    "\n",
    "Here I use `scipy.optimize.minimize` to solve the optimization problem.   \n",
    "It can be useful to read the doc for the [Linear constraint](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.LinearConstraint.html).\n",
    "It is convenient to write the two linear equality constraints in a compact form: \n",
    "\n",
    "$$ \\begin{pmatrix} 1 & 1 & ... & 1 \\\\ \\mu_1 & \\mu_2 & ... & \\mu_N \\end{pmatrix} \\cdot \n",
    "\\begin{pmatrix} w_1 \\\\ w_2 \\\\ \\vdots \\\\ w_N \\end{pmatrix} =  \\bigg( \\begin{array}{c} 1 \\\\ \\mu^P \\end{array} \\bigg)\n",
    "$$\n",
    "\n",
    "The condition $\\boldsymbol w \\geq 0$ is for an investor that is not allowed to take short positions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimizer(MU, COV, target_mu, OnlyLong=True):\n",
    "    \"\"\" Finds optimal weights for a fixed target portfolio return \"\"\"\n",
    "    \n",
    "    N = len(MU)\n",
    "    if OnlyLong == True:\n",
    "        bounds = Bounds(0, 1)\n",
    "    A = np.vstack( (np.ones(N), MU) )\n",
    "    B = np.array([1,target_mu])\n",
    "    linear_constraint = LinearConstraint( A, B, B)\n",
    "    \n",
    "    weights = np.ones(N)\n",
    "    x0 = weights/np.sum(weights) #Create x0, the initial guess for the weights\n",
    "\n",
    "    #Define the objective function\n",
    "    quadratic_form = lambda w: (w.T @ COV @ w) \n",
    "    if OnlyLong:\n",
    "        res = minimize(quadratic_form, x0=x0, method='trust-constr', constraints=linear_constraint, bounds=bounds)\n",
    "    else:\n",
    "        res = minimize(quadratic_form, x0=x0, method='trust-constr', constraints=linear_constraint)\n",
    "    return res.x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I compute the optimal weights for several values of target expected return $\\mu^P$. With these weights we can compute the standard deviation $\\sigma^P$ of the corresponding portfolio.     \n",
    "The curve of all the points $(\\sigma^P,\\mu^P)$ is called **efficient frontier**.\n",
    "\n",
    "The Sharpe ratio is a performance measure defined as\n",
    "\n",
    "$$SR = \\frac{\\mu^P - Rf}{\\sigma^P}$$\n",
    "\n",
    "where $Rf$ is the risk free rate. The line with a slope equal to the maximum Sharpe ratio is called **capital market line** (CML).     \n",
    "The point on the efficient frontier with maximum Sharpe ratio is called **tangent portfolio**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = 200\n",
    "means = np.linspace(0, np.max(MU), samples)       # vector of target expected returns\n",
    "stds = np.zeros_like(means)\n",
    "sharpe_ratio = np.zeros_like(means)\n",
    "\n",
    "for i,mn in enumerate(means):\n",
    "    w_opt = optimizer(MU, COV, mn)                 # optimal weights\n",
    "    stds[i] = np.sqrt(w_opt@COV@w_opt)\n",
    "    sharpe_ratio[i] = (mn - Rf)/stds[i]\n",
    "    \n",
    "ind_SR = np.argmax(sharpe_ratio)      # index of the maximum Sharpe Ratio\n",
    "max_SR = sharpe_ratio[ind_SR]         # maximum Sharpe ratio\n",
    "\n",
    "y = np.linspace(0, stds.max(), samples)         \n",
    "CML = Rf + max_SR * y                           # capital market line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15,5))\n",
    "plt.scatter(stds, means, linewidths=0.01, color=\"green\", label=\"Efficient Frontier\")\n",
    "for i in range(N):\n",
    "    plt.plot( cp.sqrt(COV[i,i]).value, MU[i], 'o', color=\"goldenrod\")\n",
    "    plt.annotate(f\"{data.columns[i]}\", (cp.sqrt(COV[i,i]).value, MU[i]) )\n",
    "plt.plot(y, CML, label=f\"Capital Market Line, sharpe ratio = {max_SR.round(4)}\")\n",
    "plt.plot(stds[ind_SR], means[ind_SR], 'rs', label=\"tangent portfolio\" )\n",
    "plt.legend(loc=\"upper left\" )\n",
    "plt.xlabel('Standard deviation'); plt.ylabel('Return'); \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Weights for the tangent portfolio:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>JPM</th>\n",
       "      <th>GLD</th>\n",
       "      <th>DIS</th>\n",
       "      <th>VNO</th>\n",
       "      <th>FB</th>\n",
       "      <th>UBS</th>\n",
       "      <th>KO</th>\n",
       "      <th>MCD</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>GM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.4856</td>\n",
       "      <td>0.0494</td>\n",
       "      <td>0.0002</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.464</td>\n",
       "      <td>0.0002</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.0003</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     AAPL    AMZN   GOOGL     JPM    GLD     DIS  VNO      FB     UBS   KO  \\\n",
       "0  0.4856  0.0494  0.0002  0.0001  0.464  0.0002  0.0  0.0001  0.0003  0.0   \n",
       "\n",
       "   MCD  ^GSPC      GM  \n",
       "0  0.0    0.0  0.0001  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(pd.DataFrame( [dict(zip( data.columns, optimizer(MU, COV, means[ind_SR]).round(4) ))] ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3.1'></a>\n",
    "## Optimize the Sharpe ratio\n",
    "\n",
    "Most of the time, we are not interested in the efficient frontier, but we just want to find the tangent portfolio.\n",
    "An alternative is to maximize the Sharpe ratio i.e. solve the following problem:\n",
    "\n",
    "$$  \\max_{\\mathbf w} \\; \\frac{\\mathbf w^T \\boldsymbol \\mu - Rf }{ \\sqrt{\\mathbf w^T \\mathbf \\Sigma \\, \\mathbf w} } \\quad \\text{subject to } \\quad \\mathbf w^T \\mathbf 1 = 1 \\quad \\text{and} \\quad \\boldsymbol w \\geq 0. $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = np.ones(N)\n",
    "x0 = weights/np.sum(weights)    # initial guess\n",
    "\n",
    "#Define the objective function (the negative Sharpe ratio)\n",
    "sharpe_fun = lambda w:  -(MU @ w - Rf) / np.sqrt(w.T @ COV @ w) \n",
    "bounds = Bounds(0, 1)\n",
    "linear_constraint = LinearConstraint( np.ones(N, dtype=int), 1, 1)\n",
    "res = minimize(sharpe_fun, x0=x0, method='trust-constr', constraints=linear_constraint, bounds=bounds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weights = \n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>JPM</th>\n",
       "      <th>GLD</th>\n",
       "      <th>DIS</th>\n",
       "      <th>VNO</th>\n",
       "      <th>FB</th>\n",
       "      <th>UBS</th>\n",
       "      <th>KO</th>\n",
       "      <th>MCD</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>GM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.4879</td>\n",
       "      <td>0.0486</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4635</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     AAPL    AMZN  GOOGL  JPM     GLD  DIS  VNO   FB  UBS   KO  MCD  ^GSPC  \\\n",
       "0  0.4879  0.0486    0.0  0.0  0.4635  0.0  0.0  0.0  0.0  0.0  0.0    0.0   \n",
       "\n",
       "    GM  \n",
       "0  0.0  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max Sharpe ratio =  0.5609210026947165\n",
      "optimal portfolio at sigma= 0.07327567789165933 and mean=0.04193520004945795\n"
     ]
    }
   ],
   "source": [
    "w_sr = res.x\n",
    "print(\"weights = \")\n",
    "display(pd.DataFrame( [dict(zip( data.columns, w_sr.round(4) ))] ) )\n",
    "print(\"Max Sharpe ratio = \", -sharpe_fun(w_sr))\n",
    "print(\"optimal portfolio at sigma= {} and mean={}\".format( np.sqrt(w_sr@COV@w_sr), MU@w_sr ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The weights are a bit different than before because here the maximum Sharpe ratio is more accurate. Before it was computed by grid search."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3.2'></a>\n",
    "### Optimal weights between stocks and bond\n",
    "\n",
    "Once we have computed the tangency portfolio, it is optimal to stay on the CML.      \n",
    "Let us call $R^P$ the return of a portfolio on the CML that allocates a fraction $w$ of the initial capital to the tangency portfolio (with return $R^T$) and $1-w$ to the risk-free asset $R_f$, i.e.\n",
    "\n",
    "$$ R^P = w R^T + (1-w) R_f = R_f + w (R^T-R_f) $$\n",
    "\n",
    "such that \n",
    "\n",
    "$$ \\mathbb{E}[R^P] = R_f + w (\\mathbb{E}[R^T] - R_f) \\quad \\text{and} \\quad  \n",
    "\\text{VAR}[R^P] = w^2 \\text{VAR}[R^T]. $$\n",
    "\n",
    "From these equations, given a desired level of expected return or variance, it is possible to calculate the optimal balance between the stocks portfolio (the tangency portfolio) and a risk free (a bond) asset.\n",
    "\n",
    "The following function does it. Let us give a value of expected return as input and see how it works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "`gtol` termination condition is satisfied.\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'Sharpe Ratio': 0.5609210026947165,\n",
       " 'stock weights': array([0.4879, 0.0486, 0.    , 0.    , 0.4635, 0.    , 0.    , 0.    ,\n",
       "        0.    , 0.    , 0.    , 0.    , 0.    ]),\n",
       " 'stock portfolio': {'std': 0.073276, 'mean': 0.041935},\n",
       " 'Bond + Stock weights': {'Bond': 0.5337, 'Stock': 0.4663},\n",
       " 'Total portfolio': {'std': 0.03417, 'mean': 0.02}}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimal_weights(MU, COV, Rf=Rf, w_max=1, desired_mean=0.02, desired_std=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    Compute the optimal weights for a portfolio containing a risk free asset and several stocks.\n",
      "    MU = vector of mean\n",
      "    COV = covariance matrix\n",
      "    Rf = risk free return\n",
      "    w_max = maximum weight bound for the stock portfolio\n",
      "    desired_mean = desired mean of the portfolio\n",
      "    desired_std = desired standard deviation of the portfolio\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(optimal_weights.__doc__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this function I also introduced the possibility to give an upperbound to the weights:\n",
    "\n",
    "$$0 \\leq \\boldsymbol w \\leq w_{max}$$\n",
    "\n",
    "Let us try it. We can see that although there is more diversification, the introduction of this bound reduced the Sharpe ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "`gtol` termination condition is satisfied.\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'Sharpe Ratio': 0.46269725863349787,\n",
       " 'stock weights': array([2.000e-01, 2.000e-01, 1.981e-01, 1.000e-04, 2.000e-01, 1.400e-03,\n",
       "        0.000e+00, 4.000e-04, 1.997e-01, 1.000e-04, 0.000e+00, 1.000e-04,\n",
       "        1.000e-04]),\n",
       " 'stock portfolio': {'std': 0.080421, 'mean': 0.038044},\n",
       " 'Bond + Stock weights': {'Bond': 0.4849, 'Stock': 0.5151},\n",
       " 'Total portfolio': {'std': 0.041424, 'mean': 0.02}}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bounded_porf = optimal_weights(MU, COV, Rf=Rf, w_max=0.2, desired_mean=0.02, desired_std=None)\n",
    "display(bounded_porf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bounded Weights = \n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>JPM</th>\n",
       "      <th>GLD</th>\n",
       "      <th>DIS</th>\n",
       "      <th>VNO</th>\n",
       "      <th>FB</th>\n",
       "      <th>UBS</th>\n",
       "      <th>KO</th>\n",
       "      <th>MCD</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>GM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.1981</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0014</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0004</td>\n",
       "      <td>0.1997</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.0001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   AAPL  AMZN   GOOGL     JPM  GLD     DIS  VNO      FB     UBS      KO  MCD  \\\n",
       "0   0.2   0.2  0.1981  0.0001  0.2  0.0014  0.0  0.0004  0.1997  0.0001  0.0   \n",
       "\n",
       "    ^GSPC      GM  \n",
       "0  0.0001  0.0001  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Bounded Weights = \")\n",
    "display(pd.DataFrame( [dict(zip( data.columns, bounded_porf[\"stock weights\"].round(4) ))] ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec4'></a>\n",
    "## Optimization with cvxpy\n",
    "\n",
    "The code of this section follows closely the example given in the [cvxpy website](https://colab.research.google.com/github/cvxgrp/cvx_short_course/blob/master/applications/portfolio_optimization.ipynb#scrollTo=--osR2je4bDI).     \n",
    "CVXPY uses a better solver, which as we will see it is much faster. It is also very easy to use.\n",
    "\n",
    "Here I also present an alternative and equivalent formulation of the problem:\n",
    "\n",
    "$$  \\max_{\\mathbf w} \\; \\boldsymbol \\mu^T \\mathbf w  - \\lambda \\, \\mathbf w^T \\mathbf \\Sigma \\, \\mathbf w \\quad \\text{subject to } \\quad \\mathbf w^T \\mathbf 1 = 1 \\quad \\text{and} \\quad \\boldsymbol w \\geq 0. $$\n",
    "\n",
    "where $\\lambda > 0$ represents the risk aversion coefficient of the investor. \n",
    "The choice of a positive lambda follows the common requirement to describe a risk-averse investor.     \n",
    "For $\\lambda \\to 0$, the investor tends to be more **risk-neutral**. For $\\lambda \\to \\infty$ the investor is very risk-averse and the optimal portfolio converges to the **minimum variance portfolio** i.e. the portfolio with the least variance.     \n",
    "\n",
    "From a mathematical point of view, this formulation corresponds to a problem where we want to maximize the expected return $ \\boldsymbol \\mu^T \\mathbf w$ for a fixed variance level $v = \\mathbf w^T \\mathbf \\Sigma \\, \\mathbf w$ plus the other constraints. \n",
    "We can introduce the **Lagrange multiplier** $\\lambda$ such that the objective function becomes $\\boldsymbol \\mu^T \\mathbf w  - \\lambda \\, (\\mathbf w^T \\mathbf \\Sigma \\, \\mathbf w - v)$, which is equivalent to the initial problem (since $v$ is just a constant and does not affect the weights)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = cp.Variable(N)                              # weights\n",
    "gamma = cp.Parameter(nonneg=True)\n",
    "ret = MU @ w                                    # portfolio return\n",
    "risk = cp.quad_form(w, COV)                     # portfolio variance \n",
    "objective = cp.Maximize(ret - gamma*risk)       # objective function\n",
    "constraints = [cp.sum(w) == 1, w >= 0]\n",
    "prob = cp.Problem( objective, constraints)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I replicate the results of the previous section.\n",
    "\n",
    "I run compute the optimal portfolio for seveal values of risk aversion $\\gamma$, that is equivalent to optimize for several values of portfolio standard deviations. The resulting curve is again the **efficient frontier**, where each point corresponds to a value of $\\gamma$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute efficient frontier.\n",
    "samples = 500\n",
    "std_values = np.zeros(samples)\n",
    "mean_values = np.zeros(samples)\n",
    "sharpe_ratio = np.zeros(samples)\n",
    "gamma_vals = np.logspace(0, 4, num=samples)        # several levels of risk aversion\n",
    "portfolios = []\n",
    "for i in range(samples):\n",
    "    gamma.value = gamma_vals[i]\n",
    "    prob.solve()\n",
    "    std_values[i] = cp.sqrt(risk).value\n",
    "    mean_values[i] = ret.value\n",
    "    sharpe_ratio[i] = (mean_values[i] - Rf)/std_values[i]\n",
    "    portfolios.append( w.value )\n",
    "\n",
    "ind_SR = np.argmax(sharpe_ratio)                # index of the maximum Sharpe Ratio\n",
    "max_SR = sharpe_ratio[ind_SR]                   # maximum Sharpe ratio\n",
    "y = np.linspace(0, std_values.max(), samples)         \n",
    "CML = Rf + max_SR * y                           # capital market line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15,5)); ax1 = fig.add_subplot(111)\n",
    "ax1.plot(std_values, mean_values, 'g-', label=\"Efficient Frontier\")\n",
    "ax1.plot(std_values[ind_SR], mean_values[ind_SR], 'rs', label=r\"Tangent portfolio, $\\gamma = {:.2f}$\".format(gamma_vals[ind_SR]) )\n",
    "ax1.plot(y, CML, label=f\"Capital Market Line, sharpe ratio = {max_SR.round(4)}\")\n",
    "for i in range(N):\n",
    "    ax1.plot( cp.sqrt(COV[i,i]).value, MU[i], 'o', color=\"goldenrod\")\n",
    "    ax1.annotate(f\"{data.columns[i]}\", (cp.sqrt(COV[i,i]).value, MU[i]) )\n",
    "ax1.legend(loc=\"upper left\" )\n",
    "ax1.set_xlabel('Standard deviation'); ax1.set_ylabel('Return'); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weights:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>JPM</th>\n",
       "      <th>GLD</th>\n",
       "      <th>DIS</th>\n",
       "      <th>VNO</th>\n",
       "      <th>FB</th>\n",
       "      <th>UBS</th>\n",
       "      <th>KO</th>\n",
       "      <th>MCD</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>GM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.48551</td>\n",
       "      <td>0.04903</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.46546</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      AAPL     AMZN  GOOGL  JPM      GLD  DIS  VNO   FB  UBS   KO  MCD  ^GSPC  \\\n",
       "0  0.48551  0.04903    0.0  0.0  0.46546  0.0  0.0 -0.0  0.0 -0.0 -0.0   -0.0   \n",
       "\n",
       "    GM  \n",
       "0 -0.0  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma= 3.8474265772585037\n",
      "Sharpe Ratio =  0.5609197942924549\n",
      "Standard Deviation and mean of the portfolio 0.073067 0.041818\n"
     ]
    }
   ],
   "source": [
    "print(\"Weights:\")\n",
    "display(pd.DataFrame( [dict(zip( data.columns, portfolios[ind_SR].round(5) ))] ) )\n",
    "print(\"gamma=\", gamma_vals[ind_SR]) \n",
    "print(\"Sharpe Ratio = \", max_SR)\n",
    "print(\"Standard Deviation and mean of the portfolio\", std_values[ind_SR].round(6), mean_values[ind_SR].round(6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec5'></a>\n",
    "## Probability density of the tangency portfolio\n",
    "\n",
    "What if we want to compute some probabilities? For instance the probability of losing money e.g. $\\mathbb{P}(R^P < x)$ ?\n",
    "\n",
    "Well, we do not have a closed form for the density of the portfolio. Since each $R^i$ is log-normal, then $\\sum_i w_i R^i$ is not a log-normal.      \n",
    "You can see here [wiki-related distribution](https://en.wikipedia.org/wiki/Log-normal_distribution#Related_distributions) that the sum of independent LN random variables is approximately log-normal, but not exactly log-normal. In our case the variables are correlated.\n",
    "\n",
    "We can use Monte Carlo to simulate many LN linear returns and compute the empirical density of the portfolio.\n",
    "It is convenient, in order to obtain a smooth density, to work with the **Gaussian Kernel density estimation** [KDE](Kernel density estimation). \n",
    "\n",
    "Let us generate some multivariate log-normal (LN) random variables $R_T = \\frac{S_0e^{X_T}-S_0}{S_0}$, starting from the knowledge of the multivariate normal random variables $X_T$. We previously computed the monthly mean and covariance of $X_T$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=42)\n",
    "LN_ret = np.exp( ss.multivariate_normal.rvs( mean=mu_log, cov=cov_log, size=50000 ) ) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_prob(LN_ret, w, lower_value):\n",
    "    \"\"\" Probability density of the optimal portfolio  \n",
    "    LN_ret = simulated log-returns. MxN matrix\n",
    "    w = weights vector Nx1 vector\n",
    "    lower_value = the maximum loss we are considering\n",
    "    \"\"\"\n",
    "    if LN_ret.shape[1] != w.shape[0]:\n",
    "        raise ValueError\n",
    "        \n",
    "    MU_simul = LN_ret.mean(axis=0)                     # mean of the linear returns (equal to MU)\n",
    "    COV_simul = np.cov(LN_ret, rowvar=False)           # covariance matrix   (equal to COV)   \n",
    "    Opt_portfolios = LN_ret @ w                        # portfolio linear returns\n",
    "    mu_port = MU_simul@w                               # portfolio mean\n",
    "    sig_port = np.sqrt(w @ COV_simul @ w)              # portfolio standard deviation \n",
    "    \n",
    "    x = np.linspace(Opt_portfolios.min(), Opt_portfolios.max(), 500 )\n",
    "    kde = ss.gaussian_kde(Opt_portfolios)\n",
    "    normal = ss.norm( loc=mu_port, scale=sig_port )\n",
    "\n",
    "    fig = plt.figure(figsize=(15,5))\n",
    "    plt.plot(x, kde.evaluate(x), color='salmon', label=\"KDE, loss prob={:.4f}\".format(\n",
    "        kde.integrate_box_1d(-np.inf, lower_value)) )\n",
    "    plt.plot(x, normal.pdf(x), label=\"Normal, loss prob={:.4f}\".format(normal.cdf(lower_value)))\n",
    "    plt.axvline(x=lower_value, color='grey', linestyle='--', lw=2, label=\"Maximum loss\")\n",
    "    plt.axvline(x=mu_port, color='green', linestyle='--', lw=1, label=\"Portfolio mean return\")\n",
    "    plt.axvline(x=mu_port-sig_port, color='orange', linestyle='--', \n",
    "                lw=1, label=r\"$\\pm$ standard deviation\")\n",
    "    plt.axvline(x=mu_port+sig_port, color='orange', linestyle='--', lw=1)\n",
    "    plt.title(\"Probability density of the portfolio returns\")\n",
    "    plt.xlabel('Return'); plt.ylabel('Density'); plt.legend(loc='upper right'); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prob(LN_ret=LN_ret, w=w_sr, lower_value=-0.09)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comment: \n",
    "\n",
    "- We can see that the two curves are not so different. This is because 1 month is still a small interval of time, and therefore the linear returns are approximately distributed like the log-returns (Normally distributed) and the sum of Normal distributed random variables is Normal. \n",
    "For a bigger time interval e.g. 1 year, the two curves become very very different.\n",
    "\n",
    "- The loss probability in the plot is the probability of losing more than the Maximum loss value i.e. $\\mathbb{P}(R^P < -0.9)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec6'></a>\n",
    "## Short positions - closed formula\n",
    "\n",
    "If are allowed to take short positions, we can remove the bound $\\boldsymbol w \\geq 0$ and the problem becomes:\n",
    "\n",
    "$$  \\min_{\\mathbf w} \\; \\mathbf w^T \\mathbf \\Sigma \\, \\mathbf w \\quad \\text{subject to } \\quad \\boldsymbol \\mu^T \\mathbf w = \\mu^P, \\quad \\mathbf w^T \\mathbf 1 = 1. $$\n",
    "\n",
    "Following [3] we can compute the weights and the efficient frontier in closed form.\n",
    "\n",
    "We can define the following new variables: \n",
    "\n",
    "$$ \\boldsymbol{\\Omega} = \\boldsymbol{\\Sigma}^{-1}, \\quad A = \\boldsymbol{1}^T \\boldsymbol{\\Omega} \\boldsymbol{\\mu}, \n",
    "\\quad B = \\boldsymbol{\\mu}^T \\boldsymbol{\\Omega} \\boldsymbol{\\mu}, \\quad C = \\boldsymbol{1}^T \\boldsymbol{\\Omega} \\boldsymbol{1}, \\quad D = B\\,C - A^2. \n",
    "$$\n",
    "\n",
    "The weights have the following **closed expression**:\n",
    "\n",
    "$$ \\boldsymbol{w} = \\frac{\\mu^P \\boldsymbol{\\Omega} \\bigl(C \\boldsymbol{\\mu} - A \\bigr) + \n",
    "\\boldsymbol{\\Omega} \\bigl( B-A\\boldsymbol{\\mu} \\bigr) }{D}.  $$\n",
    "\n",
    "The **efficient frontier** is a **parabola** with the following equation:\n",
    "\n",
    "$$ \\bigl(\\sigma^P \\bigr)^2 = \\frac{ C \\bigl(\\mu^P \\bigr)^2 - 2A \\mu^P + B}{D}. $$\n",
    "\n",
    "It is good to check that the covariance matrix is full rank before the inversion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The rank of the covariance matrix is: 13\n",
      "The shape of the covariance matrix is: (13, 13)\n"
     ]
    }
   ],
   "source": [
    "print(\"The rank of the covariance matrix is:\", np.linalg.matrix_rank(COV) )\n",
    "print(\"The shape of the covariance matrix is:\", COV.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "Omega = np.linalg.inv(COV)\n",
    "A = np.ones(N) @ Omega @ MU\n",
    "B = MU @ Omega @ MU\n",
    "C = Omega.sum()\n",
    "D = B*C - A**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "target_mu = 0.1\n",
    "weights_th = (target_mu * Omega @ (C*MU-A)  + Omega @ (B-MU*A) )/D    # theoretical weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Theoretical weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>JPM</th>\n",
       "      <th>GLD</th>\n",
       "      <th>DIS</th>\n",
       "      <th>VNO</th>\n",
       "      <th>FB</th>\n",
       "      <th>UBS</th>\n",
       "      <th>KO</th>\n",
       "      <th>MCD</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>GM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.2458</td>\n",
       "      <td>0.3685</td>\n",
       "      <td>0.5282</td>\n",
       "      <td>0.5597</td>\n",
       "      <td>0.9733</td>\n",
       "      <td>0.1442</td>\n",
       "      <td>-0.2223</td>\n",
       "      <td>-0.272</td>\n",
       "      <td>0.4089</td>\n",
       "      <td>0.1547</td>\n",
       "      <td>-0.1562</td>\n",
       "      <td>-2.9257</td>\n",
       "      <td>0.193</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     AAPL    AMZN   GOOGL     JPM     GLD     DIS     VNO     FB     UBS  \\\n",
       "0  1.2458  0.3685  0.5282  0.5597  0.9733  0.1442 -0.2223 -0.272  0.4089   \n",
       "\n",
       "       KO     MCD   ^GSPC     GM  \n",
       "0  0.1547 -0.1562 -2.9257  0.193  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(pd.DataFrame( [dict(zip( data.columns, weights_th.round(4) ))] ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Numerical weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>AMZN</th>\n",
       "      <th>GOOGL</th>\n",
       "      <th>JPM</th>\n",
       "      <th>GLD</th>\n",
       "      <th>DIS</th>\n",
       "      <th>VNO</th>\n",
       "      <th>FB</th>\n",
       "      <th>UBS</th>\n",
       "      <th>KO</th>\n",
       "      <th>MCD</th>\n",
       "      <th>^GSPC</th>\n",
       "      <th>GM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.2458</td>\n",
       "      <td>0.3685</td>\n",
       "      <td>0.5282</td>\n",
       "      <td>0.5597</td>\n",
       "      <td>0.9733</td>\n",
       "      <td>0.1442</td>\n",
       "      <td>-0.2223</td>\n",
       "      <td>-0.272</td>\n",
       "      <td>0.4089</td>\n",
       "      <td>0.1547</td>\n",
       "      <td>-0.1562</td>\n",
       "      <td>-2.9257</td>\n",
       "      <td>0.193</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     AAPL    AMZN   GOOGL     JPM     GLD     DIS     VNO     FB     UBS  \\\n",
       "0  1.2458  0.3685  0.5282  0.5597  0.9733  0.1442 -0.2223 -0.272  0.4089   \n",
       "\n",
       "       KO     MCD   ^GSPC     GM  \n",
       "0  0.1547 -0.1562 -2.9257  0.193  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(pd.DataFrame( [dict(zip( data.columns, optimizer(MU, COV, target_mu, False).round(4) ))] ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let us compute the efficient frontier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = 50\n",
    "means = np.linspace(-0.1, 0.17, samples)            # vector of target expected returns\n",
    "stds = np.zeros_like(means)\n",
    "\n",
    "for i,mn in enumerate(means):\n",
    "    w_opt = optimizer(MU, COV, mn, OnlyLong=False)                 # optimal weights\n",
    "    stds[i] = np.sqrt(w_opt@COV@w_opt)                             # std of the portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15,6))\n",
    "y = np.linspace(-0.1, 0.2, 400)\n",
    "x = np.linspace(0, 0.23, samples)         \n",
    "y, x = np.meshgrid(x, y)\n",
    "CS = plt.contour(y, x, y**2 - (C*x**2-2*A*x+B)/D , [0], colors='k', alpha=0.7)\n",
    "plt.clabel(CS, inline=1, fontsize=10); CS.collections[0].set_label(\"Theoretical efficient frontier\")\n",
    "plt.scatter(stds, means, linewidths=0.1, color=\"green\", label=\"Numerical efficient Frontier\")\n",
    "for i in range(N):\n",
    "    plt.plot( cp.sqrt(COV[i,i]).value, MU[i], 'o', color=\"goldenrod\")\n",
    "    plt.annotate(f\"{data.columns[i]}\", (cp.sqrt(COV[i,i]).value, MU[i]) )\n",
    "plt.xlim([0.03,0.19])\n",
    "plt.legend(loc=\"upper left\" ); plt.title(\"Efficient frontier - Short positions allowed\")\n",
    "plt.xlabel('Standard deviation'); plt.ylabel('Return'); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Attilio Meucci (2005) *Risk and asset allocation*. \n",
    "\n",
    "[2] D. Ruppert, D. Matteson (2015) *Statistics and Data analysis for financial engineering*\n",
    "\n",
    "[3] Robert Merton (1970) *An analytical derivation of the efficient portfolio frontier*"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
